The single degree of freedom (SDOF) systems have been studied usually via ordinary mathematical tools like calculus, for inquiring about the effects of various pulses like rectangular pulse, step force, triangular pulse, etc., on their responses. In this paper, the SDOF systems such as an undamped mechanical oscillator as well as an undamped electrical oscillator exposed to a triangular pulse have been contemplated and their responses have been determined by the integral Rohit transform (RT). The graphs of responses of SDOF systems versus time have been plotted. It is inferred from the graphs that even though the amplitude of triangular pulse is decreasing linearly, the response of SDOF systems is periodically increasing and decreasing. This paper put forward a new technique for determining the response of SDOF systems (undamped oscillators) exposed to a triangular pulse and reveals that RT is an effective tool for analyzing the SDOF systems.